Monty Hall Problem

The Monty Hall Problem is a classic problem in probability. It is all over the Internet. Beside being a famous problem, it stirred up a huge controversy when it was posted in a column hosted by Marilyn vos Savant in Parade Magazine back in 1990. vos Savant received negative letters in the thousands, many of them from readers who were mathematicians, scientists and engineers with PhD degrees! It is possible to get this problem wrong (or get in a wrong path in reasoning).